Details

Time bar (total: 15.3s)

sample60.0ms

Algorithm
intervals
Results
34.0ms278×body80valid
10.0ms97×body80nan

simplify141.0ms

Counts
1 → 1
Iterations
IterNodes
done160
7160
6159
5152
4140
3108
263
136
020

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.5b

localize148.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
1.1b
(- (sqrt (fma -4 (* c a) (* b b))) b)
22.2b
(sqrt (fma -4 (* c a) (* b b)))
22.2b
(sqrt (fma -4 (* c a) (* b b)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
78×prod-diff
71×add-sqr-sqrt
67×*-un-lft-identity
61×add-cube-cbrt
50×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
3×diff-log distribute-lft-out--
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 flip--
1×associate--l- neg-sub0 neg-log
Counts
4 → 165
Calls
4 calls:
13.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
16.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
3.0ms
(sqrt (fma -4 (* c a) (* b b)))
5.0ms
(sqrt (fma -4 (* c a) (* b b)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
125.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
113.0ms
(sqrt (fma -4 (* c a) (* b b)))
106.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify1.2s

Counts
177 → 177
Iterations
IterNodes
done2002
32002
2965
1425
0194

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.7b

localize130.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (sqrt (fma -4 (* c a) (* b b))) b) 2) a)
0.6b
(fma -4 (* c a) (* b b))
1.1b
(- (sqrt (fma -4 (* c a) (* b b))) b)
22.2b
(sqrt (fma -4 (* c a) (* b b)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
18×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×div-sub
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log fma-udef flip-- associate-/l/
Counts
4 → 179
Calls
4 calls:
42.0ms
(/ (/ (- (sqrt (fma -4 (* c a) (* b b))) b) 2) a)
0.0ms
(fma -4 (* c a) (* b b))
15.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
3.0ms
(sqrt (fma -4 (* c a) (* b b)))

series444.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ (/ (- (sqrt (fma -4 (* c a) (* b b))) b) 2) a)
96.0ms
(fma -4 (* c a) (* b b))
96.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
140.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify1.3s

Counts
191 → 191
Iterations
IterNodes
done2007
32007
21582
1619
0278

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.7b

localize148.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (- (sqrt (fma -4 (* a c) (* b b))) b) (/ 1/2 a))
0.6b
(fma -4 (* a c) (* b b))
1.1b
(- (sqrt (fma -4 (* a c) (* b b))) b)
22.2b
(sqrt (fma -4 (* a c) (* b b)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
31×*-un-lft-identity
27×add-cube-cbrt
18×prod-diff
17×sqrt-prod
13×associate-*r*
10×times-frac
9×add-cbrt-cube add-exp-log
7×pow1
6×fma-neg associate-*l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u difference-of-squares
3×flip3-- flip--
2×frac-times associate-*l/ prod-exp cbrt-unprod distribute-lft-out-- unswap-sqr
1×cbrt-undiv rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log div-exp pow-prod-down associate-*r/ *-commutative fma-udef div-inv
Counts
4 → 111
Calls
4 calls:
25.0ms
(* (- (sqrt (fma -4 (* a c) (* b b))) b) (/ 1/2 a))
0.0ms
(fma -4 (* a c) (* b b))
7.0ms
(- (sqrt (fma -4 (* a c) (* b b))) b)
1.0ms
(sqrt (fma -4 (* a c) (* b b)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(* (- (sqrt (fma -4 (* a c) (* b b))) b) (/ 1/2 a))
81.0ms
(fma -4 (* a c) (* b b))
103.0ms
(- (sqrt (fma -4 (* a c) (* b b))) b)
98.0ms
(sqrt (fma -4 (* a c) (* b b)))

simplify1.1s

Counts
123 → 123
Iterations
IterNodes
done2001
32001
21234
1398
0174

prune810.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.7b

localize214.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (fma -4 (* c a) (* b b))) b)
1.1b
(- (sqrt (fma -4 (* c a) (* b b))) b)
22.2b
(sqrt (fma -4 (* c a) (* b b)))
22.2b
(sqrt (fma -4 (* c a) (* b b)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
36×prod-diff
34×add-cube-cbrt
32×sqrt-prod
12×fma-neg
8×add-log-exp
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log flip-- distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
13.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
13.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
2.0ms
(sqrt (fma -4 (* c a) (* b b)))

series417.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
103.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
83.0ms
(sqrt (fma -4 (* c a) (* b b)))
132.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify1.1s

Counts
128 → 128
Iterations
IterNodes
done2001
42001
3908
2311
1168
085

prune957.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.7b

regimes405.0ms

Accuracy

95.4% (0.4b remaining)

Error of 12.5b against oracle of 12.1b and baseline of 20.7b

bsearch105.0ms

Steps
ItersRangePoint
6
1.459596161815481e+138
1.5335818162182465e+139
3.3660304103825555e+138

simplify15.0ms

Iterations
IterNodes
done45
145
039

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.7s8761×body80valid
619.0ms2940×body80nan